The ability to explain decisions made by AI systems is highly sought after, especially in domains where human lives are at stake such as medicine or autonomous vehicles. While it is always possible to approximate the input-output relations of deep neural networks with human-understandable rules or a post-hoc model, the discovery of the double descent phenomena suggests that no such approximation will ever map onto the actual mechanistic functioning of deep neural networks. Double descent indicates that deep neural networks typically operate by smoothly interpolating between data points rather than by extracting a few high level rules. As a result neural networks trained on complex real world data are inherently hard to interpret and prone to failure if used outside their domain of applicability (ie, for extrapolation). To show how we might be able to trust AI despite these problems, we introduce the concept of self-explaining AI. Self-explaining AIs are capable of providing a human-understandable explanation of each decision along with confidence levels for both the decision and explanation. Some difficulties to this approach along with possible solutions are sketched. Finally, we argue it is also important that AI systems warn their user when they are asked to perform outside their domain of applicability.